Geometrical Considerations

Abstract

This chapter provides an introduction (at a somewhat general level) to some rather fundamental geometrical ideas and results. Some knowledge of this material is an important prerequisite for assimilating ideas in several areas of statistics, including linear statistical models and multivariate analysis.

Among those who teach and write about the more theoretical aspects of linear statistical models, there is a considerable difference of opinion about the extent to which geometrical ideas should be emphasized (relative to “algebraic” ideas). Those who prefer a “geometrical approach” (e.g., Scheffé 1959, Christensen 1996) argue that it is more general, more elegant, and (perhaps most important) more intuitive. Those who prefer a more algebraic approach (e.g., Searle 1971) find it to be more rigorous, more concrete, more palatable to those with a limited mathematical background, and (perhaps most important) more suggestive of computational approaches.